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The partial differential equation u_(xy)+(alphau_x-betau_y)/(x-y)=0.

The partial differential equation u_t=Du_(xx)+u-u^2.

The system of partial differential equations S_t=SxS_(xx).

The system of partial differential equations U_t=U·U_(xx)+U·LambdaU.

Let A be a C^*-algebra, then an element u in A is called a partial isometry if uu^*u=u.

The partial differential equation u_(tt)-u_(xx)-u+u^3=0.

The partial differential equation u_(tt)-u_(xx)=epsilon(u_t-u_t^3).

The partial differential equation u_t+u_x-6uu_x-u_(txx)=0.

The partial differential equation u_(yy)=yu_(xx).

A set in Euclidean space R^d is convex set if it contains all the line segments connecting any pair of its points. If the set does not contain all the line segments, it is ...